Simple yet comprehensive unified physical model of the 2-D electron gas in delta-doped and uniformly doped high electron mobility transistors

This paper presents a new approach to model the 2-DEG concentration (ns) versus gate voltage (VG) behavior and the equilibrium 2-DEG concentration (ns0) in a HEMT. The approach results in a model which is 'comprehensive' in the following sense. It is valid for both delta-doped and uniformly doped HEMT's. It captures all the three ns-VG nonlinearities (subthreshold, gradual pinchoff, and gradual saturation), and the effects of all the device parameters including temperature, in relation expressing ns as an explicit closed-form integrable function of VG having continuous first derivatives; thus, the function readily yields a device current-voltage/capacitance-voltage (I-V/C-V) model which can be incorporated in softwares meant for simulation of circuits, particularly of the analog variety. The simple model is shown to predict the results of complex numerical calculations and experiments. The closed-form ns0 expression of the model is the first of its kind reported for delta-doped HEMT's, and reveals an interesting feature unexposed by earlier ns0 models: the reciprocal of ns0 in both delta-doped and uniformly doped devices decreases linearly with reduction in spacer width, and saturates at low spacer widths in some delta-doped devices. It is shown that the measured ns0 in delta-doped devices is predicted correctly if the electrons in the V-shaped well are assumed to be trapped at the donor sites rather than to be filling the conduction subbands.